I am confuse in finding Argumnet of Complex Number

[urduworld]

hi PF

1. (2+2i) First Quadrant
2. (-2+2i) Second Quadrant
3. (-2-2i) Third Quadrant
4. (2-2i) Fourth Quadrant

consider (2+1i) then Tan^-1(2/2) which will be 45 degree
if we consider (-2+2i) then it will be -45 degree but angle will not -45 degree actually we get answer by adding or deducting 180 or some like this i want to know what we have to add or subtract i am confuse about this

also what to do for third and fourth quadrants

i want to know this for Log of complex number and Polar form
Please help me
Thanks in advance :)

 

[Mark44]

hi PF

1. (2+2i) First Quadrant
2. (-2+2i) Second Quadrant
3. (-2-2i) Third Quadrant
4. (2-2i) Fourth Quadrant

consider (2+1i) then Tan^-1(2/2) which will be 45 degree
if we consider (-2+2i) then it will be -45 degree but angle will not -45 degree actually we get answer by adding or deducting 180 or some like this i want to know what we have to add or subtract i am confuse about this

You seem to be confused between the reference angle and the angle as measured from the positive real axis. For 2 + 2i, the reference angle and the angle itself are both 45 degrees, or pi/4. For -2 + 2i, the reference angle is also 45 degrees (not -45 degrees), but since the angle is in the second quadrant, the actual angle is 180 - 45 = 135 degrees, or 3pi/4. If you calculate the angle using the inverse tangent function, you have t^-1(-2/2) = -45 degrees. You have to add 180 degrees to this, because your angle is in the 2nd quadrant, so you get 180 + (-45) = 135 degrees again.

The range of the inverse tangent function is (-90, 90) (in degrees), or (-pi/2, pi/2), so if your angle is not in the 1st or 4th quadrants you have to adjust the value to get the angle you need.

If your angle is in the third quadrant, as it is for -2 - 2i, you'll have tan^-1(-2/(-2)) = 45 degrees. The actual angle is 180 + 45 = 225 degrees, or 5pi/4.

also what to do for third and fourth quadrants

i want to know this for Log of complex number and Polar form
Please help me
Thanks in advance :)

 

[urduworld]

this means i have to add 180 in all the condition except if it is in first

 

[Mark44]

I didn't talk about a fourth quadrant angle, but maybe you can figure out what you need to do. If z = 2 - 2i, the argument would be -45 degrees. As a positive angle, what would it be?